Application of a generalized formula of linear regression for construction of one-parameter models of aerosol extinction

Nikolay N. Shchelkanov

doi:10.1117/12.606290

15 December 2004 Application of a generalized formula of linear regression for construction of one-parameter models of aerosol extinction

Nikolay N. Shchelkanov

Author Affiliations +

Proceedings Volume 5743, Eleventh International Symposium on Atmospheric and Ocean Optics/Atmospheric Physics; (2004) https://doi.org/10.1117/12.606290
Event: Eleventh International Symposium on Atmospheric and Ocean Optics/Atmospheric Physics, 2004, Tomsk, Russian Federation

Abstract

The generalized formula is presented allowing to obtain the regression coefficients of the linear equation Y=K₀+K₁X for the general case, when the scatter of points in the correlation diagram of the values X and Y has been caused by both their random errors of measurements and uncontrolled physical factors. All knows formulas for the regression coefficients are the partial cases of the obtained formula. The ways are proposed and the formulas for the regression coefficients are the partial cases of the obtained formula. The ways are proposed and the formulas are presented for estimating the rms errors of the measured values involving in the formula for calculating the regression coefficients from the experiments data. It is shown that the generalized formula makes it possible to obtain the stable, reliable and physically correct one-parameter models of the aerosol extinction. The obtained formula is interesting for the specialists in processing experimental data and can be used for their correct physical interpretation independently of the field of knowledge.

Citation Download Citation

Nikolay N. Shchelkanov "Application of a generalized formula of linear regression for construction of one-parameter models of aerosol extinction", Proc. SPIE 5743, Eleventh International Symposium on Atmospheric and Ocean Optics/Atmospheric Physics, (15 December 2004); https://doi.org/10.1117/12.606290

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